Detecting infeasible solutions is an important challenge in closed-box multiobjective bilevel optimization (MOBO) due to a lower-level (LL) optimization problem used as a constraint (along with equality and inequality constraints) in an upper-level optimization. In this context, a feasible solution is an optimal solution to the LL problem, typically addressed using evolutionary algorithms (EAs) (or other metaheuristics) for complex scenarios. Since metaheuristics do not guarantee optimality, then infeasible solutions are inherently reported. This article introduces a novel data-driven framework to automatically identify infeasible solutions reported by bilevel EAs (BEA) when addressing any MOBO problem. This framework operates without imposing strong assumptions on objectives or constraints, making it versatile and easy to implement. Besides, our approach uses solutions reported by one or multiple BEAs to detect and eliminate possible infeasible solutions. This approach helps to enhance algorithm comparison by eliminating infeasible solutions before applying existing performance indicators. The framework is successfully applied to several MOBO problems, including two real-world instances from specialized literature, solved by four different BEAs. Results suggest that the proposed framework advances the field of bilevel evolutionary optimization, offering a tool for promoting fair algorithmic comparisons and ensuring solution feasibility without requiring a deep understanding of the problem context.

Wrapper approaches for feature selection are known for their high performance, but the drawback of high computational cost is presented. This work proposes using cost-reduction mechanisms applied to the permutational-based Differential Evolution (DE-FSPM) algorithm for feature selection. Two proposals considering fixed and incremental sampling fraction strategies are considered to reduce the cost of evaluating an individual. A memory mechanism for avoiding repeated evaluations is included. The success-history parameter adaptation for Differential Evolution (SHADE) procedure adapted to the permutational search space is applied in two additional proposals. Eighteen datasets were used for experimentation. The fixed sampling fraction proposal with the memory mechanism reached competitive accuracy results while requiring less computational time. The sampling strategies could effectively reduce the number of dataset instances used for evaluation. In addition, the memory mechanism avoids a fraction of the evaluations in the search process. The results show that two simple mechanisms can effectively decrease the computational cost of a wrapper approach for feature selection without diminishing its performance.

Convolutional neural networks (CNNs) have shown a competitive performance in medical imaging applications, such as image segmentation. However, choosing an existing architecture capable of adapting to a specific dataset is challenging and requires design expertise. Neural architecture search (NAS) is employed to overcome these limitations. NAS uses techniques to design the Neural Networks architecture. Typically, the models’ weights optimization is carried out using a continuous loss function, unlike model topology optimization, which is highly influenced by the specific problem. Genetic programming (GP) is an evolutionary algorithm (EA) capable of adapting to the topology optimization problem of CNNs by considering the attributes of its representation. A tree representation can express complex connectivity and apply variation operations. This article presents a tree-based GP algorithm for evolving CNNs based on the well-known U-Net architecture producing compact and flexible models for medical image segmentation across multiple domains. This proposal is called NAS / GP / U-Net (NASGP-Net). NASGP-Net uses a cell-based encoding and U-Net architecture as a backbone to construct CNNs based on a hierarchical arrangement of primitive operations. Our experiments indicate that our approach can produce remarkable segmentation results with fewer parameters regarding fixed architectures. Moreover, NASGP-Net presents competitive results against NAS methods. Finally, we observed notable performance improvements based on several evaluation metrics, including dice similarity coefficient (DSC), intersection over union (IoU), and Hausdorff distance (HD).

Hierarchical decision-making can be observed in different research areas where two optimization levels define a bilevel optimization problem. For instance, in a supply chain production and distribution problem, two decision-makers control these processes respectively, where one company is dedicated only to the distribution of the products, and the other is dedicated to the production of these products. This kind of problem is considered challenging. This work is then on the solution of the Bilevel Multi-Depot Vehicle Routing Problem (BiMDVRP), in which multiple depots need to deliver cargo to cover the demand of many retailers subject to the production plants to meet the demand of each depot optimally. A hybrid genetic algorithm to solve the aforementioned bilevel planning problem is proposed in this work. We use the available information on the problem to implement heuristic mechanisms to improve the results reported by state-of-the-art algorithms. We propose a representation based on groups for the feasible configuration of each depot, due to constraints related to a depot being satisfied. The experimental results show that group-based coding quickly obtains high-quality solutions for the set of instances used in our experimentation setup.

The Flexible Job-Shop Scheduling Problem is one of the most studied problems in the specialized literature. Since it was put forth for the first time, there have been multiple variants and constraints proposed in addition to the classic implementation. As an NP-Hard problem, the best way to solve the FJSP is through heuristic algorithms. In recent years there has been an increasing interest in solving NP-Hard problems by using Genetic Algorithms and the Flexible Job-Shop Problem is not an exception. There are different approaches based on a GA for solving the FJSP. This paper revisits the research on solution representation and, aiming to solve the FJSP, proposes a new encoding scheme that represents each solution as a sequencing paired list. The proposed scheme aims to improve the performance of a genetic algorithm toward better solutions within the search space. The encoding was tested on benchmarks commonly found in the literature. The experimental results show that this encoding scheme fulfills its objective and can be used as an alternative to other widespread encodings such as MSOS (Machine Selection and Operation Sequence).

This article presents the optimal tuning of an Active Disturbance Rejection Controller (ADRC) applied to the tracking control of a servo system. The ADRC consists of a Luenberger Observer coupled with a Disturbance Observer. Its purpose is to reject the disturbances affecting the servo system and to impose a desired closed-loop dynamics. Previous results on this controller focus only on its stability analysis. Moreover, finding the controller parameters that provide optimal performance is difficult. For the foregoing reasons, this work proposes using the Particle Swarm Optimization (PSO) algorithm to tune the parameters of the ADRC. The restrictions imposed on the particles are obtained from the stability analysis of the ADRC. This allows discarding those solutions leading to closed-loop instability. Therefore, the algorithm delivers solutions where a fitness function is minimized, and the closed-loop system is stable. Finally, realtime experiments on a laboratory prototype show the performance of the proposed tuning method.

Optimization makes processes, systems, or products more efficient, reliable, and with better outcomes. A popular topic on optimization today is multiobjective bilevel optimization (MOBO). In MOBO, an upper level problem is constrained by the solution of a lower level one. The problem at each level can include multiple conflicting objective functions and its own constraints. This survey aims to study the solution approaches proposed to solve MOBO problems, including exact methods and approximate techniques such as metaheuristics (MHs). This work explores classical literature to investigate why most classical methods, theories, and algorithms focus on linear and some convex MOBO problems to solve the optimistic MOBO. Moreover, we study and propose a taxonomy of MH-based frameworks for solving some MOBO instances, highlighting the pros and cons of five main approaches. Finally, a growing interest in MOBO has been detected in the optimization community. A significant number of possible applications and solution approaches establish an early research line to find solutions to these types of problems.

In a mixed-integer nonlinear programming problem, integer restrictions divide the feasible region into discontinuous feasible parts with different sizes. Evolutionary Algorithms (EAs) are usually vulnerable to being trapped in larger discontinuous feasible parts. In this work, an improved version of an Estimation of Distribution Algorithm (EDA) is developed, where two new op-erations are proposed. The first one establishes a link between the learning-based histogram model and the$\varepsilon$-constrained method. Here, the constraint violation level of the$\varepsilon$-constrained method is used to explore the smaller discontinuous parts and form a better statistical model. The second operation is the hybridization of the EDA with a mutation operator to generate offspring from both the global distribution information and the parent information. A benchmark is used to test the performance of the improved proposal. The results indicated that the proposed approach shows a better performance against other tested EAs. This new proposal solves to a great extent the influence of the larger discontinuous feasible parts, and improve the local refinement of the real variables.

Convolutional neural networks (CNNs) have shown outstanding results in different application tasks. However, the best performance is obtained when customized CNNs architectures are designed, which is labor intensive and requires highly specialized knowledge. Over three decades, neuroevolution (NE) has studied the application of evolutionary computation to optimize artificial neural networks (ANNs) at different levels. It is well known that the encoding of ANNs highly impacts the complexity of the search space and the optimization algorithms’ performance as well. As NE has rapidly advanced toward the optimization of CNNs topologies, researchers face the challenging duty of representing these complex networks. Furthermore, a compilation of the most widely used encoding methods is nonexistent. In response, we present a comprehensive review on thestate-of-the-artof encodings for CNNs.

Many real-world problems can be modeled using graphs. This representation allows us to understand some important aspects of problem behavior through the calculation of different measures. The energy of a graph is an invariant measure that has gained interest in network analysis due to its recent applications, then it is interesting to know the structural properties that make two graphs with similar energies.In this work we propose the search for almost-equienergetic graphs using evolutionary algorithms for Erdös-Rényi networks and trees. The proposed evolutionary algorithms are able to obtain almost-equienergetic graphs in larger instances with respect to traditional methods and the results lead to analyze interesting properties of the graphs found.

The use of biomedical images for the training of various Deep Learning (DL) systems oriented to health has reported a competitive performance. However, DL needs a large number of images for a correct generalization and, particularly in the case of biomedical images, these can be scarce. Generative Adversarial Networks (GANs) as Data Augmenting tools have reaped significant results to improve performance in tasks that involve the use of this kind of image. However, the architectural design of these generative models in the biomedical image area has been usually relegated to the expertise of researchers. Moreover, GANs are affected by training instability that may lead to poor quality results. This paper presents a neuroevolution algorithm based on Particle Swarm Optimization for the design and training of GANs for the generation of biomedical Chest X-Ray (CXR) images of pneumonia caused by COVID-19. The proposed approach allows having a swarm of GANs topologies, where each one of them grows progressively while being trained at the same time. The fitness value is based on the Frechet Inception Distance (FID). The proposed algorithm is able to obtain better FID results compared to handcrafted GANs for the synthesis of CXR images.

The identification of subnetworks of interest-or active modules-by integrating biological networks with molecular profiles is a key resource to inform on the processes perturbed in different cellular conditions. We here propose MOGAMUN, a Multi-Objective Genetic Algorithm to identify active modules in MUltiplex biological Networks. MOGAMUN optimizes both the density of interactions and the scores of the nodes (e.g., their differential expression). We compare MOGAMUN with state-of-the-art methods, representative of different algorithms dedicated to the identification of active modules in single networks. MOGAMUN identifies dense and high-scoring modules that are also easier to interpret. In addition, to our knowledge, MOGAMUN is the first method able to use multiplex networks. Multiplex networks are composed of different layers of physical and functional relationships between genes and proteins. Each layer is associated to its own meaning, topology, and biases; the multiplex framework allows exploiting this diversity of biological networks. We applied MOGAMUN to identify cellular processes perturbed in Facio-Scapulo-Humeral muscular Dystrophy, by integrating RNA-seq expression data with a multiplex biological network. We identified different active modules of interest, thereby providing new angles for investigating the pathomechanisms of this disease. Availability: MOGAMUN is available at https://github.com/elvanov/MOGAMUN and as a Bioconductor package at https://bioconductor.org/packages/release/bioc/html/MOGAMUN.html. Contact: [email protected].

The efficient speed regulation of four-bar mechanisms is required for many industrial processes. These mechanisms are hard to control due to the highly nonlinear behavior and the presence of uncertainties or disturbances. In this paper, different Pareto-front approximation search approaches in the adaptive controller tuning based on online multiobjective metaheuristic optimization are studied through their application in the four-bar mechanism speed regulation problem. Dominance-based, decomposition-based, metric-driven, and hybrid search approaches included in the algorithms, such as nondominated sorting genetic algorithm II, multiobjective evolutionary algorithm based on decomposition and differential evolution, S-metric selection evolutionary multiobjective algorithm, and nondominated sorting genetic algorithm III, respectively, are considered in this paper. Also, a proposed metric-driven algorithm based on the differential evolution and the hypervolume indicator (HV-MODE) is incorporated into the analysis. The comparative descriptive and nonparametric statistical evidence presented in this paper shows the effectiveness of the adaptive controller tuning based on online multiobjective metaheuristic optimization and reveals the advantages of the metric-driven search approach.

One of the challenges that appear in solving constrained optimization problems is to quickly locate the search areas of interest. Although the initial solutions of any optimization algorithm have a significant effect on its performance, none of the existing initialization methods can provide direct information about the objective function and constraints of the problem to be solved. In this paper, a technique for generating initial solutions is proposed, which provides useful information about the behavior of both the objective function and the constraints. Based on such information, an automatic mechanism for selecting individuals, from the search areas of interest, is introduced. The proposed method is adopted with different evolutionary algorithms and tested on the CEC2006 and the CEC2010 test problems. The results obtained show the benefits of the proposed method in enhancing the performance, and reducing the average computational time, of several algorithms with respect to their versions adopting other initialization techniques.

This paper presents an experimental comparison of nine boundary constraint-handling methods found in the specialized literature added to differential evolution when solving four mechanical design optimization problems. The experimental part considers a comparison of final results besides performance measures used in evolutionary constrained optimization as well as the number of vectors and variables repaired. The Kruskal-Wallis non-parametric test and the Bonferroni post-hoc test are computed to validate the findings. The final results suggest that the Projection method provides a better overall performance when compared with other approaches. However, Centroid 1+1 was the method which promotes less repairs.

A Bilevel Optimization Problem (BOP) is related to two optimization problems in a hierarchical structure. A BOP is solved when an optimum of the upper level problem is found, subject to the optimal response of the respective lower level problem. This paper presents a metaheuristic method assisted by a kernel interpolation numerical technique to approximate optimal solutions of a BOP. Two surrogate methods approximate upper and lower level objective functions on solutions obtained by a population-based algorithm adapted to save upper level objective function evaluations. Some theoretical properties about kernel interpolation are used to study global convergence in some particular BOPs. The empirical results of this approach are analyzed when representative test functions for bilevel optimization are solved. The overall performance provided by the proposal is competitive.

This paper presents an extension of a preliminary study about differential evolution in the solution of robust optimization over time problems. A set of test instances with four dynamics with three different time window values are solved by six differential evolution variants, whose parameters were set by means of a tool based on statistical methods so as to promote a fair comparison. The results are compared against one particle swarm optimization algorithm found as very competitive when solving robust optimization over time problems. The results obtained suggest that the most popular differential evolution variant, DE/rand/1/bin, is the most competitive when compared with the particle swarm optimization algorithm.

This work presents a population-based metaheuristic approach using Tykhonov regularization and a quasi-Newton method, called Quasi-Newton Bilevel Centers Algorithm (QBCA), to deal with bilevel optimization problems. Tykhonov regularization for bilevel optimization is adopted to handle problems with nonunique lower level solutions. Besides, a quasi-Newton method is adapted to deal with infeasible solutions in the lower level. The performance of this proposal is assessed by using representative test functions for bilevel optimization. The results based on accuracy and number of evaluations are promising when QBCA is compared against the efficient algorithm BLEAQ-II.

Dynamic constrained optimization problems (DCOPs) have gained researchers attention in recent years because a vast majority of real world problems change over time. There are studies about the effect of constrained handling techniques in static optimization problems. However, there lacks any substantial study in the behavior of the most popular constraint handling techniques when dealing with DCOPs. In this paper we study the four most popular used constraint handling techniques and apply a simple Differential Evolution (DE) algorithm coupled with a change detection mechanism to observe the behavior of these techniques. These behaviors were analyzed using a common benchmark to determine which techniques are suitable for the most prevalent types of DCOPs. For the purpose of analysis, common measures in static environments were adapted to suit dynamic environments. While an overall superior technique could not be determined, certain techniques outperformed others in different aspects like rate of optimization or reliability of solutions.

An empirical comparison is conducted to analyze three different elements involved in population diversity management in constrained numerical optimization problems: (1) optimization algorithms, (2) constraint-handling techniques and (3) diversity promotion techniques. Combinations of basic algorithm versions, differential evolution, and real-coded genetic algorithm, applying feasibility rules, ε-Constrained method and stochastic ranking as constraint-handling techniques, and also implementing a diversity promotion technique, were generated. Each combination (48 in total) was tested by solving 36 well-known benchmark problems. The final results highlight the combination of differential evolution, ε-Constrained method and a couple of non-disruptive diversity promotion techniques, as the most promising combinations.

This paper presents an empirical study comparing the performance of thirty-five boundary constraint-handling methods (BCHM) for PSO in constrained optimization, which were tested in a set of thirty-six well-known constrained problems. Each BCHM is composed as an hybrid consisting of one position update techniques and one velocity update strategy. Results show that the hybrid method that relocates the particles through a position update technique called Centroid and modifies its velocity through the Deterministic Back strategy is able to promote better final results and improving both, the approach to the feasible region and the ability to generate better feasible solutions.

In this paper, two existing constraint handling approaches are compared. The constraint handling approaches are based on the same principle of preferring feasible solution candidates over infeasible but they differ in the case of two infeasible solution candidates. One approach calculates the sum of constraint violations, whereas the other approach uses Pareto-dominance of constraint violations. Comparison of the constraint handling approaches is done experimentally using Differential Evolution (DE) algorithm. DE, as many other evolutionary algorithms, contains control parameters to be set by the user. Besides using fixed control parameter values, also an Exponential Weighting Moving Average (EWMA) control parameter adaptation technique is used. Experimental results reveal that neither of the constraint handling approaches can be judged to be better than the other. What is surprising, also EWMA cannot be judged to improve performance when applied to constraints. It is rather causing more uncertainty according to the results.

In this article, a brief literature review of Full Model Selection (FMS) for temporal data is presented. An analysis of FMS approaches which use evolutionary algorithms to exploit and explore the vast search space found in this kind of problem is presented. The primary motivation of this review is to highlight the scarce published works of FMS in temporal databases. Moreover, a taxonomy for the tasks derived of FMS is proposed and chosen to discuss the different revised approaches. Also, the most representative assessment measures for model selection are described. From the literature review, a set of opportunities and challenges research is presented in the temporal FMS area.

Differential Evolution (DE) is a population-based Evolutionary Algorithm (EA) for solving optimization problems over continuous spaces. Many optimization problems are constrained and have a bounded search space from which some vectors leave when the mutation operator of DE is applied. Therefore, it is necessary the use of a boundary constraint-handling method (BCHM) in order to repair the invalid mutant vectors. This paper presents a generalized and improved version of the Centroid BCHM in order to keep the search within the valid ranges of decision variables in constrained numerical optimization problems (CNOPs), which has been tested on a robust and comprehensive set of experiments that include a variant of DE specialized in dealing with CNOPs. This new version, named Centroid [Formula: see text], relocates the mutant vector in the centroid formed by K random vectors and one vector taken from the population that is within or near the feasible region. The results show that this new version has a major impact on the algorithm’s performance, and it is able to promote better final results through the improvement of both, the approach to the feasible region and the ability to generate better solutions.

In this work, three modifications are proposed to improve the performance of the Variable Interaction Identification for Constrained problems (VIIC), a technique to detect interacting variables in large scale constrained numerical optimization problems. The changes proposed are: (1) the optimization of a single variable arrangement (the original VIIC needs to find an arrangement of variables for the objective function and also for each constraint), (2) two new strategies to generate a new arrangement, instead of the random generator of the original VIIC, and (3) simulated annealing as an optimizer instead of the greedy search adopted in the original VIIC. The results indicate the viability of using just one variable arrangement and the good performance provided by the two proposed strategies in the search, particularly combined with VIIC's original greedy search.

A study on three BSO algorithm versions: Brain Storm Optimization Algorithm (BSO), Modified Brain Storm Optimization Algorithm (MBSO) and Simple Modified Brain Storm Optimization Algorithm (SMBSO), for constrained numerical optimization problems is presented in this paper. The aim of the study is to know the performance of this recent Swarm Intelligence (SI) algorithm on constrained search spaces. The feasibility rules, ε-constrained method, and stochastic ranking are used as constraint-handling techniques. The performance of each version is analysed by solving 24 well-known benchmark problems. The final results suggest MBSO and the ε-constrained method as a good option to deal with constrained problems.

Cervical Cytology or Pap Smear is the most popular technique for pre-diagnosis of cervical cancer. However, this technique has a high rate of false negative. As a consequence, it is necessary to complement it with other tests like Colposcopy. In some studies about the colposcopy test, it has been proposed that temporal changes intrinsic to the colposcopic image can be used to automatically characterize cervical lesions. In this document, a methodology to segment colposcopic images based on these temporal changes produced by the acetowhite reaction is presented in order to support to the colposcopist in the early detection of cervical cancer. This methodology consists in two stages: (1) a preprocessing stage, where several steps (extraction of time series, dimensionality reduction, classification process and a post-processing stage) are done to decrease problems or noise (specular reflection and keratosis) that can be seen as the acetowhite reaction, and (2) a segmentation stage where the active contour model (Snake) is used, changing the greedy search mechanism by a global search mechanism (evolutionary programming). The experiments were developed using only one colposcopic image and all the image sequence extracted from the colposcopy process. Results show that our methodology is a competitive tool to support to the colposcopist in the early detection of cervical cancer, providing one step towards the decrease of the mortality rate of this disease.

A highly competitive micro evolutionary algorithm to solve unconstrained optimization problems called μJADE (micro adaptive differential evolution), is adapted to deal with constrained search spaces. Two constraint-handling techniques (the feasibility rules and the ε-constrained method) are tested in μJADE and their performance is analyzed. The most competitive version is then compared against two highly-competitive algorithms for constrained optimization when solving a well-known set of 36 test problems, and also against a small population algorithm tested on another well-known set of thirteen problems. The results show that μJADE provides a better performance when coupled with the ε-constrained method and also that its results are competitive against those provided by state-of-the-art approaches.

In this paper a new boundary constraint-handling technique called “centroid” is proposed to keep the search within the valid ranges of decision variables in a constrained numerical optimization problem. Such technique is based on computing the centroid of three solutions within the search space, one taken from the population and two generated at random. A comparison of the proposed technique in three experiments against other approaches found in the specialized literature is carried out by using a well-known scalable benchmark of 18 test problems. The results show that the proposed technique is able to promote better final results and improving both, the approach to the feasible region and the ability to generate better solutions.

In this paper a multiobjective differential evolution algorithm called Generalized Differential Evolution is extended to solve dynamic multiobjective optimization problems (DMOPs). The proposed algorithm combines the ideas of the generalized differential evolution and the artificial immune system to create a hybrid algorithm which uses the advantages of both approaches. When a change is detected in the environment by a solution reevaluation mechanism, an immune response is activated. The approach is compared against other dynamic multiobjective algorithms in a recently proposed benchmark. Experimental results show that the proposed approach can track the environmental change and has a very competitive performance solving different types of DMOPs.

Repair methods, which usually require feasible solutions as reference, have been employed by Evolutionary Algorithms to solve constrained optimization problems. In this work, a novel repair method, which does not require feasible solutions as reference and inspired by the differential mutation, is added to an algorithm which uses two variants of differential evolution to solve dynamic constrained optimization problems. The proposed repair method replaces a local search operator with the aim to improve the overall performance of the algorithm in different frequencies of change in the constrained space. The proposed approach is compared against other recently proposed algorithms in an also recently proposed benchmark. The results show that the proposed improved algorithm outperforms its original version and provides a very competitive overall performance with different change frequencies.

In this work a differential evolution algorithm is adapted to solve dynamic constrained optimization problems. The approach is based on a mechanism to detect changes in the objective function and/or the constraints of the problem so as to let the algorithm to promote the diversity in the population while pursuing the new feasible optimum. This is made by combining two popular differential evolution variants and using a memory of best solutions found during the search. Moreover, random-immigrants are added to the population at each generation and a simple hill-climber-based local search operator is applied to promote a faster convergence to the new feasible global optimum. The approach is compared against other recently proposed algorithms in an also recently proposed benchmark. The results show that the proposed algorithm provides a very competitive performance when solving different types of dynamic constrained optimization problems.

The stepsize value is one of the most sensitive parameters in the bacterial foraging optimization algorithm when solving constrained numerical optimization problems. In this paper, four stepsize control mechanisms are proposed and analyzed in the modified bacterial foraging optimization algorithm. The first one is based on a random value which remains fixed during the search, the second one generates a random value per cycle, the third one is based on a nonlinear decreasing function and the last one is an adaptive approach. Seven experiments are proposed to evaluate the abilities of each mechanism to: (1) obtain competitive final results, (2) find feasible solutions, (3) find the feasible global optimum, (4) promote successful swims, and (5) decrease the constraint violation. A comparison against two state-of-the-art algorithms is considered to evaluate the performance of the most competitive control mechanism. A well-known set of constrained numerical optimization problems is used in the experiments as well as six performance measures. The results obtained show that the control mechanism based on the nonlinear decreasing function is the most competitive and provides the ability to generate better solutions late in the search.

A new differential evolution algorithm for single objective optimization is presented in this paper. The proposed algorithm uses a self-adaptation mechanism for parameter control, divides its population into more subpopulations, applies more DE strategies, promotes population diversity, and eliminates the individuals that are not changed during some generations. The experimental results obtained by our algorithm on the benchmark consisting of 25 test functions with dimensions D = 10, D = 30, and D = 50 as provided for the CEC 2013 competition and special session on Real Parameter Single Objective Optimization are presented.

This paper presents a memetic algorithm for solving constrained numerical optimization problems. The proposed approach uses differential evolution as a global search algorithm, which was improved with a mathematical programming method called Powell's conjugate direction as a local search operator. To the best of the authors' knowledge, this is the first attempt to use such mathematical programming method within differential evolution for constrained optimization. The proposed algorithm was tested on 36 test problems used in the special session on “Single Objective Constrained Real-Parameter Optimization” in CEC'2010. The proposed algorithm is able to find competitive results with respect to the winner algorithm in that session.

Recently, Particle Swarm Optimizer (PSO) has become a popular tool for solving constrained optimization problems. However, there is no guarantee that PSO will perform consistently well for all problems and will not be trapped in local optima. In this paper, a PSO algorithm is introduced that uses two new mechanisms, the first one to maintain a better balance between intensification and diversification and the second one to escape from local solutions. Furthermore, all the basic parameters are determined self-adaptively. The performance of the proposed algorithm is analyzed by solving the CEC2010 constrained optimization problems. The algorithm shows consistent performance, and is superior to other state-of-the-art algorithms.

A review of the bacterial foraging optimization algorithm used to solve numerical constrained optimization problems is presented in this paper. After an introduction to the algorithm and its main elements, a taxonomy of constraint-handling techniques is presented and adopted to discuss the different approaches based on the algorithm. Aspects related to the most important elements of the algorithm with respect to a constrained search space (e.g., constraint-handling technique, stepsize, tumble-swim operator, reproduction process) are analyzed. Based on the findings of this literature review, some fertile paths of research are presented.

Differential Evolution (DE) is an algorithm capable of solving complex optimization problems with and without constraints. As many of the population-based algorithms, DE is based on operators that evolve a numerical population through search operators. The differential mutation, one of the basic operators in the original version of the algorithm, provides population diversity through the evolution. In this paper we propose an extended version of a previously proposed hybrid DE including know two different mutation operators, which are not applied simultaneously. The first of them, our main contribution, is based on the exploitation of feasible areas to identify promising regions of search space. The second mutation operator is the classic differential mutation and it is applied towards produce a balance between exploration and exploitation as well as to improve the individuals obtained with our operator. An experimental study was performed by considering 18 functions presented for the “Single Objective Constrained Real-Parameter Optimization” of the special session of CEC2010. The results are compared with those obtained by Takahama and Sakai, winners that CEC2010 special session with εDEag algorithm. The obtained results show that our proposed approach is capable of finding solutions of higher quality for scalable problems of dimension 30 whereas the results for dimension 10 remains competitive with εDEag.

This paper presents a differential evolution (DE) algorithm for real-parameter optimization. The algorithm includes the self-adaptive jDE algorithm with one of its strongest extensions, population reduction, combined with multiple mutation strategies using a structured population. The two mutation strategies used are run dependent on the population size, which is reduced with growing function evaluation number. The population is structured with a separate part where only DE/best strategy is executed and then the best vectors are exchanged with the main population part. Algorithm performance assessment results are presented for 10, 30, and 50 dimension settings for all of the 28 problems included in the Problem Definitions and Evaluation Criteria for the CEC 2013 Special Session and Competition on Real-Parameter Optimization.

This paper presents the addition of an adaptive stepsize value and a local search operator to the modified bacterial foraging algorithm (MBFOA) to solve constrained optimization problems. The adaptive stepsize is used in the chemotactic loop for each bacterium to promote a suitable sampling of solutions and the local search operator aims to promote a better trade-off between exploration and exploitation during the search. Three MBFOA variants, the original one, another with only the adaptive stepsize and a third one with both, the adaptive stepsize and also the local search operator are tested on a set of well-known benchmark problems. Furthermore, the most competitive variant is compared against some representative nature-inspired algorithms of the state-of-the-art. The results obtained provide evidence on the utility of each added mechanism, while the overall performance of the approach makes it a viable option to solve constrained optimization problems.

In this paper, we present a surrogate-based multi-objective evolutionary optimization approach to optimize airfoil aerodynamic designs. Our approach makes use of multiple surrogate models which operate in parallel with the aim of combining their features when solving a costly multi-objective optimization problem. The proposed approach is used to solve five multiobjective airfoil aerodynamic optimization problems. We compare the performance of a multi-objective evolutionary algorithm with surrogates with respect to the same approach without using surrogates. Our preliminary results indicate that our proposal can achieve a substantial reduction in the number of objective function evaluations, which has obvious advantages for dealing with expensive objective functions such as those involved in aeronautical optimization problems.

Nowadays, the solution of multiobjective optimization problems in aeronautical and aerospace engineering has become a standard practice. These two fields offer highly complex search spaces with different sources of difficulty, which are amenable to the use of alternative search techniques such as metaheuristics, since they require little domain information to operate. From the several metaheuristics available, multiobjective evolutionary algorithms (MOEAs) have become particularly popular, mainly because of their availability, ease of use, and flexibility. This paper presents a taxonomy and a comprehensive review of applications of MOEAs in aeronautical and aerospace design problems. The review includes both the characteristics of the specific MOEA adopted in each case, as well as the features of the problems being solved with them. The advantages and disadvantages of each type of approach are also briefly addressed. We also provide a set of general guidelines for using and designing MOEAs for aeronautical and aerospace engineering problems. In the final part of the paper, we provide some potential paths for future research, which we consider promising within this area.

This paper presents an adaptation of a novel algorithm based on the foraging behavior of honey bees to solve constrained numerical optimization problems. The modifications focus on improving the way the feasible region is approached by using a new operator which allows the generation of search directions biased by the best solution so far. Furthermore, two dynamic tolerances applied in the constraint handling mechanism help the algorithm to the generation of feasible solutions. The approach is tested on a set of 24 benchmark problems and its behavior is compared against the original algorithm and with respect to some state-of-the-art algorithms.

A novel algorithm to solve constrained real-parameter optimization problems, based on the Artificial Bee Colony algorithm is introduced in this paper. The operators used by the three types of bees (employed, onlooker and scout) are modified in such a way that more diverse and convenient solutions are generated. Furthermore, a dynamic tolerance control mechanism for equality constraints is added to the algorithm in order to facilitate the approach to the feasible region of the search space. Finally, two simple local search operators are applied to the best solution found so far. The algorithm, called Elitist-ABC, is tested on 18 test problems based on the experimental design proposed for the CEC'2010 competition on constrained real-parameter optimization. The results obtained are discussed and some conclusions are drawn.

In this paper, we present a novel Multi-Objective Evolutionary Algorithm (MOEA) called MODE-LD+SS, which combines Differential Evolution with local dominance and a scalar selection mechanism for improving both its convergence rate and its distribution of solutions along the Pareto front. In order to assess the performance of the proposed approach, we use a set of standard test functions and performance measures taken from the specialized literature. Results are compared with respect to three MOEAs representative of the state-of-the-art in the area: NSGA-II, SPEA2, and MOEA/D.

In this paper we present the addition of parameter control in a differential evolution algorithm for constrained optimization. Three parameters are self-adapted by encoding them within each individual and a fourth parameter is controlled by a deterministic approach. A set of experiments are performed in order (1) to determine the performance of the modified algorithm with respect to its original version, (2) to analyze the behavior of the self-adaptive parameter values and (3) to compare it with respect to state-of-the-art approaches. Based on the obtained results, some findings regarding the values for the DE parameters as well as for the parameters related with the constraint-handling mechanism are discussed.

In this paper, we present an improved Genetic Algorithm (GA) that is able to find the shortest addition chains for a given exponent e. Two new variation operators (special two-point crossover and a local-search-like mutation) are proposed as a means to improve the GA search capabilities. Furthermore, the usage of an improved repair mechanism is applied to the process of generating the initial population of the algorithm. The proposed approach is compared on a set of test problems with two state-of-the-art evolutionary heuristic-based approaches recently published. Finally, the modified GA is used to find the optimal addition chain length for a small collection of ldquohardrdquo exponents. The results obtained are competitive and even better in the more difficult instances of the exponentiation problem that were considered here.

This paper presents a novel evolutionary approach to solve numerical optimization problems, called Adaptive Evolution (AEv). AEv is a new micro-population-like technique because it uses small populations (less than 10 individuals). The two main mechanisms of AEv are elitism and adaptive behavior. It has an adaptive parameter to adjust the balance between global exploration, local exploitation and elitism. Its two crossover operators allow a newly-generated offspring to be parent of other offspring in the same generation. AEv requires the fine-tuning of two parameters (several state-of-the-art approaches use at least three). AEv is tested on a set of 10 benchmark functions with 30 decision variables and it is compared with respect to some state-of-the-art algorithms to show its competitive performance.

In this paper, we propose a novel approach to solve constrained optimization problems based on particle swarm optimization (PSO). First, an empirical comparison of the most popular PSO variants is presented as to select the most convenient among them. After that, the PSO variant chosen is improved in: (1) its parameter control with a dynamic proposal as to promote a better exploration of the search space and to avoid premature convergence and (2) its constraint-handling mechanism by using multiobjective concepts as to promote a better approach to the feasible region. The algorithm is tested on a set of 13 well-known benchmark problems and the obtained performance is compared against some PSO variants and state-of-the-art approaches. Based on the results presented some conclusions are drawn and the future work is established.

This paper presents a comparison of four bio- inspired algorithms (all seen as search engines) with a similar constraint-handling mechanism (Deb's feasibility rules) to solve constrained optimization problems. The aim is to analyze the performance of traditional versions of each algorithm based on both, final results and on-line behavior. A set of 24 well- known benchmark problems are used in the experiments. Quality and consistency of results per each algorithm are investigated. Furthermore, two performance measures (number of evaluations to reach a feasible solution and progress ratio inside the feasible region) are utilized to compare the on-line behavior of each approach. Based on the obtained results, some conclusions are established.

In this paper, we present an ant system algorithm variant designed to solve the job shop scheduling problem. The proposed approach is based on a recent biological study which showed that natural ants can count their steps when they build the path between the nest and their food source. Experiments using a set of well-known job shop scheduling problems and a comparison against state-of-the-art techniques show that the proposed approach can reduce the number of evaluations performed without a degradation of performance. Additionally, our proposed approach reduces the number of parameters that need to be tuned by the user (specifically the parameters that balance the importance between the pheromone trail and heuristic values), with respect to the original ant system algorithm.

October 01 2007 Evolutionary Computation. A Unified Approach. Kenneth A. De Jong. (2006, MIT Press.) £32.95, $50.00, 256 pages Efrén Mezura-Montes Efrén Mezura-Montes Search for other works by this author on: This Site Google Scholar Author and Article Information Efrén Mezura-Montes Online Issn: 1530-9185 Print Issn: 1064-5462 © 2007 Massachusetts Institute of Technology2007 Artificial Life (2007) 13 (4): 423–426. https://doi.org/10.1162/artl.2007.13.4.423 Cite Icon Cite Permissions Share Icon Share Twitter LinkedIn Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Peer Review Search Site Citation Efrén Mezura-Montes; Evolutionary Computation. A Unified Approach. Kenneth A. De Jong. (2006, MIT Press.) £32.95, $50.00, 256 pages. Artif Life 2007; 13 (4): 423–426. doi: https://doi.org/10.1162/artl.2007.13.4.423 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search nav search search input Search input auto suggest search filter All ContentAll JournalsArtificial Life Search Advanced Search This content is only available as a PDF. © 2007 Massachusetts Institute of Technology2007 Article PDF first page preview Close Modal You do not currently have access to this content.

In this paper, we present a Differential-Evolution based approach to solve constrained optimization problems. The aim of the approach is to increase the probability of each parent to generate a better offspring. This is done by allowing each solution to generate more than one offspring but using a different mutation operator which combines information of the best solution in the population and also information of the current parent to find new search directions. Three selection criteria based on feasibility are used to deal with the constraints of the problem and also a diversity mechanism is added to maintain infeasible solutions located in promising areas of the search space. The approach is tested in a set of test problems proposed for the special session on Constrained Real Parameter Optimization. The results obtained are discussed and some conclusions are established.

In this paper, we present an empirical comparison of some Differential Evolution variants to solve global optimization problems. The aim is to identify which one of them is more suitable to solve an optimization problem, depending on the problem's features and also to identify the variant with the best performance, regardless of the features of the problem to be solved. Eight variants were implemented and tested on 13 benchmark problems taken from the specialized literature. These variants vary in the type of recombination operator used and also in the way in which the mutation is computed. A set of statistical tests were performed in order to obtain more confidence on the validity of the results and to reinforce our discussion. The main aim is that this study can help both researchers and practitioners interested in using differential evolution as a global optimizer, since we expect that our conclusions can provide some insights regarding the advantages or limitations of each of the variants studied.

In this paper, we present an empirical study whose aim is twofold: (1) to analyze the on-line behavior of two state-of-the-art approaches for constrained optimization, whose results provided in a well-known benchmark were competitive, in order to identify features of a problem which makes it difficult to solve when using an evolutionary algorithm and (2) to propose a new set of problems whose features cover those sources of difficulty. The on-line behavior analyzed consists on using three performance measures to know how fast the technique reaches the feasible region and to also know the capabilities of the algorithm to improve feasible solutions previously found. Besides, we analyze the ability of the approaches to maintain diversity (to have solutions inside and outside the feasible region as well). Based on the obtained results we propose a set of eleven test problems (either artificial or real-world problems) taken from the literature in order to re-test the approaches. The results are discussed and some conclusions are drawn.

In this paper, we incorporate a diversity mechanism to the differential evolution algorithm to solve constrained optimization problems without using a penalty function. The aim is twofold: (1) to allow infeasible solutions with a promising value of the objective function to remain in the population and also (2) to increase the probabilities of an individual to generate a better offspring while promoting collaboration of all the population to generate better solutions. These goals are achieved by allowing each parent to generate more than one offspring. The best offspring is selected using a comparison mechanism based on feasibility and this child is compared against its parent. To maintain diversity, the proposed approach uses a mechanism successfully adopted with other evolutionary algorithms where, based on a parameter Sr a solution (between the best offspring and the current parent) with a better value of the objective function can remain in the population, regardless of its feasibility. The proposed approach is validated using test functions from a well-known benchmark commonly adopted to validate constraint-handling techniques used with evolutionary algorithms. The statistical results obtained by the proposed approach are highly competitive (based on quality, robustness and number of evaluations of the objective function) with respect to other constraint-handling techniques, either based on differential evolution or on other evolutionary algorithms, that are representative of the state-of-the-art in the area. Finally, a small set of experiments were made to detect sensitivity of the approach to its parameters.

This work presents a simple multimembered evolution strategy to solve global nonlinear optimization problems. The approach does not require the use of a penalty function. Instead, it uses a simple diversity mechanism based on allowing infeasible solutions to remain in the population. This technique helps the algorithm to find the global optimum despite reaching reasonably fast the feasible region of the search space. A simple feasibility-based comparison mechanism is used to guide the process toward the feasible region of the search space. Also, the initial stepsize of the evolution strategy is reduced in order to perform a finer search and a combined (discrete/intermediate) panmictic recombination technique improves its exploitation capabilities. The approach was tested with a well-known benchmark. The results obtained are very competitive when comparing the proposed approach against other state-of-the art techniques and its computational cost (measured by the number of fitness function evaluations) is lower than the cost required by the other techniques compared.

In this paper, we propose the use of a simple evolution strategy (SES) (i.e., a (1 + /spl lambda/)-ES with self-adaptation that uses three tournament rules based on feasibility) coupled with a diversity mechanism to solve constrained optimization problems. The proposed mechanism is based on multiobjective optimization concepts taken from an approach called the niched-Pareto genetic algorithm (NPGA). The main advantage of the proposed approach is that it does not require the definition of any extra parameters, other than those required by an evolution strategy. The performance of the proposed approach is shown to be highly competitive with respect to other constraint-handling techniques representative of the state-of-the-art in the area when using a set of well-known benchmarks.

This paper presents a simple (1 + /spl lambda/) evolution strategy and three simple selection criteria to solve engineering optimization problems. This approach avoids the use of a penalty function to deal with constraints. Its main advantage is that it does not require the definition of extra parameters, other than those used by the evolution strategy. A self-adaptation mechanism allows the algorithm to maintain diversity during the process in order to reach competitive solutions at a low computational cost. The approach was tested in four well-known engineering design problems and compared against several penalty-function-based approaches and other state-of-the-art technique. The results obtained indicate that the proposed technique is highly competitive in terms of quality, robustness and computational cost.